Question
Answer
$$(x^2+2xy+y^2)^2-3x^2y^2=x^4+4x^3y+3x^2y^2+4xy^3+y^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+2xy+y^2)^2-3x^2y^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4+4x^3y+6x^2y^2+4xy^3+y^4-3x^2y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^4+4x^3y+3x^2y^2+4xy^3+y^4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+2xy+y^2}\right) $ by each term in $ \left( x^2+2xy+y^2\right) $. $$ \left( \color{blue}{x^2+2xy+y^2}\right) \cdot \left( x^2+2xy+y^2\right) = \\ = x^4+2x^3y+x^2y^2+2x^3y+4x^2y^2+2xy^3+x^2y^2+2xy^3+y^4 $$ |
| ② | Combine like terms: $$ x^4+ \color{blue}{2x^3y} + \color{red}{x^2y^2} + \color{blue}{2x^3y} + \color{green}{4x^2y^2} + \color{orange}{2xy^3} + \color{green}{x^2y^2} + \color{orange}{2xy^3} +y^4 = \\ = x^4+ \color{blue}{4x^3y} + \color{green}{6x^2y^2} + \color{orange}{4xy^3} +y^4 $$ |
| ③ | Combine like terms: $$ x^4+4x^3y+ \color{blue}{6x^2y^2} +4xy^3+y^4 \color{blue}{-3x^2y^2} = x^4+4x^3y+ \color{blue}{3x^2y^2} +4xy^3+y^4 $$ |
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